Analysis of the contraction of series and parallel muscles working against elastic loads

The purpose of the present study was to analyze the manner in which series and parallel arrangements of respiratory muscles, contracting together, augment the forces and displacements applied to external elastic loads over those produced by a single muscle contracting alone. We first developed a series of mathematical expressions to describe the behavior of various arrangements of muscles contracting against elastic loads. We then compared the predictions of these equations with the results from experiments in which the forces and displacements produced by simple arrangements of muscles were measured. Both theoretical and experimental results indicate that, against high elastic loads, parallel arrangements of muscle strips produce greater forces and greater displacements than do single muscles; parallel arrangements do not, however, significantly increase the displacement or force applied to low elastic loads. Conversely, series arrangements result in greater forces and greater displacement of low loads, but are no better than single muscles when contracting against high loads. Against moderate loads parallel and series arrangements of muscles appear to be equivalent in generating forces and displacements during contraction. This analysis suggests that a major determinant of the effects of contraction of various networks of inspiratory muscles is the magnitude and character of the respiratory impedance against which these muscles must work. The primary difference between series and parallel arrangements of muscles is that muscles arranged in series are most effective against low elastic loads and muscles in parallel act most effectively against high loads.